Rajan, who took up his post as central bank governor earlier this month, is challenged with boosting India's economy amid sky-high inflation, a rapidly weakening rupee, increased borrowing costs, a faltering stock market and its slowest economic growth in a decade.

India is also particularly vulnerable due to its $88 billion current account deficit, which reflects the nation's tendency to import many more goods than it exports and leaves it heavily reliant on foreign capital.

But Rajan isn't wasting any time. In his first day on the job, he announced reforms that should make it much easier for new banks to be licensed. He also took steps to support the rupee, including a new central bank facility to encourage commercial banks to accept more deposits from overseas.

The former chief economist at the International Monetary Fund seems undeterred by the challenges he faces, and has said he isn't afraid of making difficult choices.

"Some of the actions I take will not be popular. The governorship of the central bank is not meant to win one votes or Facebook likes," he said.